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1. The income of A, B and C are in the ratio 7 : 9 : 12 and their spending are in the ratio 8 : 9 : 15. If A saves $\frac{1}{4}$ th of his income then the savings of A, B and C are in the ratio of = ?

A. 56 : 99 : 69

B. 69 : 56 : 99

C. 99 : 56 : 69

D. 99 : 69 : 56

Solution:

Let income of A, B and C are 7x, 9x and 12x respectively
and expenditure of A, B and C are 8y, 9y and 15y respectively

\begin{aligned} \Rightarrow Income of, \\ A \times \frac{1}{4} = Saving of A (given) \\ \Rightarrow 7 x - 8 y = 7 x \times \frac{1}{4} \\ \Rightarrow 28 x - 32 y = 7 x \\ \Rightarrow 21 x = 32 y \\ \Rightarrow x : y = 32 : 21 \end{aligned}

∴ The ratio of savings of A, B and C
⇒ (7x - 8y) : (9x - 9y) : (12x - 15y)
⇒ (7 × 32 - 8 × 21) : (9 × 32 - 9 × 21) : (12 × 32 - 15 × 21)
⇒ (224 - 168) : (288 - 189) : (384 - 315)
⇒ 56 : 99 : 69

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